A regret-based approach to non-stationary discrete stochastic optimization

This paper presents regret-based adaptive search algorithms for non-stationary simulation-based discrete optimization problems. The proposed algorithm relies on a potential-based sampling strategy that prescribes how to successively take samples from the search space. Performance analysis shows that the randomly evolving set of global optimizers can be properly tracked by showing that the worst case regret can be kept arbitrarily small infinitely often. The proposed scheme allows temporal correlation of the simulation data, and assumes no functional properties on the objective function. Numerical examples show that performance gains are obtained in both convergence speed and efficiency as compared with random search, simulated annealing, and pure exploration methods.